A delta-sigma (ΔΣ) modulator is one type of analog-to-digital converter. Within ΔΣ modulators generally, there is a specific type called a continuous-time ΔΣ modulator (CT-DSM). Stability in these CT-DSMs is an important concern. To control the stability of a CT-DSM, direct feedback coefficients and flash digital-to-analog (DAC) timing coefficients are commonly used.
Direct feedback—or sometimes called excess loop delay compensation—is used to ensure loop stability when the modulator's center frequency is not at fs/4 (i.e., a quarter of the sampling frequency). As the fastest feedback term in a modulator, the direct feedback coefficient affects the noise transfer function (NTF) outside of the pass-band. A suboptimal direct feedback coefficient increases out-of-band spectral power and hence decreases the stability of the modulator. Due to process variation and manufacturing tolerances, the optimum direct feedback coefficient for maximum stability can differ between chips.
Similar to the direct feedback coefficient, the flash DAC timing coefficient—sometimes called flash clock delay—affects the out-of-band response of a CT-DSM. A suboptimal flash clock delay coefficient leads to peaks in a modulator's out-of-band spectrum, which degrades the stability of the system.
CT-DSMs, unlike their discrete-time ΔΣ modulator cousins, are timing sensitive and can become unstable if the direct feedback (excess loop delay compensation) and flash DAC timing coefficients are not set correctly. Due to process variation, which changes the optimal modulator parameters, performance is often sacrificed in the form of less aggressive noise shaping to ensure the modulator is stable with a large input.
A more stable modulator allows for a larger maximum-stable input. This larger maximum-stable input permits an increased maximum signal-to-noise ratio (SNR) for such a modulator over a less stable modulator. Alternatively, for a same maximum-stable input power as a less stable modulator, a more stable modulator can employ a more aggressive noise shaping, due to the increased stability, leading to an increased SNR.
Both the direct feedback coefficient and the flash DAC timing coefficient can be tuned in a laboratory environment. However, it is difficult to tune these coefficients in the field because the spectrum of the associated modulator is not known.
A previous effort to solve this problem designed blocks, such as direct feedback and flash clock delay circuits, that desensitize modulator stability to process variation. Because of inherent differences between simulation and actual silicon, the direct feedback and flash DAC timing coefficients for these circuits need to be lab-tuned to find their optimum values. Thus, if those coefficients are not affected by process variation, the lab-tuned values can be used for production releases. However, if the coefficients are sensitive to process variation, a less aggressive noise-shaping should be used to ensure the modulator is stable for the designed maximum-stable input power level.